# On Tian-Todorov lemma and its applications to deformation of CR-structures

## TL;DR

This paper introduces a new Tian-Todorov lemma for CR-structure deformations and demonstrates its use in proving unobstructedness of certain CR-manifolds, aligning with Tian-Todorov's original methodology.

## Contribution

A novel Tian-Todorov lemma for CR-structures and its application to establish deformation unobstructedness under the $d'd''$-lemma.

## Key findings

- New Tian-Todorov lemma for CR-structures
- Reproof of deformation unobstructedness
- Alignment with Tian-Todorov's original approach

## Abstract

We give a new Tian-Todorov lemma on deformations of CR-structures and use it to reprove the deformation unobstructedness of normal compact strongly pseudoconvex CR-manifold under the assumption of $d'd''$-lemma, more faithfully following Tian-Todorov's approach.